We have celebrated birthdays for both of my children at Chef Mickeys and they were great. They gave them a autographed picture placemat of all the characters. They brought out a cupcake with a candle and sang happy birthday. The table was decorated with confetti when we sat down, we let them know before we got there it would be for a birthday. We had our reservations for breakfast both times.
I would have to say it depends on a lot of info we don't have. How old is the child? What is their favorite character? Favorite type of food? Favorite theme? Shy or Adventurous?
For a kid that loves fish or Finding Nemo, consider Coral Reef. They make a personalized menu and you can get a diver to hold a sign in the tank. A child that loves animals, might enjoy Boma and watching the animals on the Savannah, or Rainforest Cafe. The dinosaur lover might prefer the new T-Rex. Maybe the cowboy lover would love WCC...... I could go on & on, but I'm sure you get the point.
Find something that "fits" your child and when you make your ADR's, be sure to tell them about the birthday (in the case of Coral Reef, call the restaurant directly to request the diver & menu) All of the restaurants will do something to make the meal special for a birthday kid.
I would also go with Chef Mickeys, I think they also let the kids with a birthday dance with the characters for a special song (or at least they did something like that in the past). Anything you pick the kids will love, its Disney and there will be characters, you can't go wrong!